-5.4x^2+8.1x+9=0

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Solution for -5.4x^2+8.1x+9=0 equation: 


Simplifying
-5.4x2 + 8.1x + 9 = 0

Reorder the terms:
9 + 8.1x + -5.4x2 = 0

Solving
9 + 8.1x + -5.4x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-5.4 the coefficient of the squared term: 

Divide each side by '-5.4'.
-1.666666667 + -1.5x + x2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + -1.5x + 1.666666667 + x2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + -1.5x + x2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + -1.5x + x2 = 0 + 1.666666667
-1.5x + x2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
-1.5x + x2 = 1.666666667

The x term is -1.5x.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5x + 0.5625 + x2 = 1.666666667 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = 1.666666667 + 0.5625

Combine like terms: 1.666666667 + 0.5625 = 2.229166667
0.5625 + -1.5x + x2 = 2.229166667

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = 2.229166667

Calculate the square root of the right side: 1.493039406

Break this problem into two subproblems by setting 
(x + -0.75) equal to 1.493039406 and -1.493039406.


Subproblem 1
x + -0.75 = 1.493039406

Simplifying
x + -0.75 = 1.493039406

Reorder the terms:
-0.75 + x = 1.493039406

Solving
-0.75 + x = 1.493039406

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.75' to each side of the equation.
-0.75 + 0.75 + x = 1.493039406 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = 1.493039406 + 0.75
x = 1.493039406 + 0.75

Combine like terms: 1.493039406 + 0.75 = 2.243039406
x = 2.243039406

Simplifying
x = 2.243039406


Subproblem 2
x + -0.75 = -1.493039406

Simplifying
x + -0.75 = -1.493039406

Reorder the terms:
-0.75 + x = -1.493039406

Solving
-0.75 + x = -1.493039406

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.75' to each side of the equation.
-0.75 + 0.75 + x = -1.493039406 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = -1.493039406 + 0.75
x = -1.493039406 + 0.75

Combine like terms: -1.493039406 + 0.75 = -0.743039406
x = -0.743039406

Simplifying
x = -0.743039406


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.243039406, -0.743039406}

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